In layman's terms:
There are two (basically) parts of an OS. One is the part the user sees and interacts with. This is called userspace. The other part is where the OS works with memory and CPU resources and schedules slices of time for each user's jobs to work. This is called kernelspace.
Microsoft designed Windows such that things that userspace processes can directly engage processes in kernelspace.
As a result a slew of viruses and trojans are able to be accessed by a user and then the malware jumps into kernelspace and invades system-level processes. This allows the malware to run with system-level permissions and hide itself from the user.
Unix and unix-like operating systems have a completely different and much more restrictive set of rules for this kind of thing.
Microsoft really hasn't ever figured out the right way to separate those sets of privileges. Each version of Windows seems to get a little better, but even Vista has the same kinds of problems while Unix has pretty much been immune from this kind of attack.
The obvious question: Why? Was it to make their system, more "user" friendly?